Materials Science. Chapter 7: Mechanical Properties. Common States of Stress. Engineering Stress. Ft F. A o ISSUES TO ADDRESS... σ = F A o.

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1 In the Name f Gd Materials Science Dr Mhammad Heidari-Rarani Chapter 7: Mechanical Prperties ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead f lad and defrmatin? Elastic behavir: When lads are small, hw much defrmatin ccurs? What materials defrm least? Plastic behavir: At what pint des permanent defrmatin ccur? What materials are mst resistant t permanent defrmatin? Tughness and ductility: What are they and hw d we measure them? Chapter 7 - Chapter 7 - Engineering Stress Tensile stress, : Shear stress, τ: t t Area, A Area, A s Cmmn States f Stress Simple tensin: cable A = crss sectinal area (when unladed) = t lb = f r A in riginal area befre lading t N m τ = s A s Stress has units: N/m r lb f /in t Chapter 7-3 = A Trsin (a frm f shear): drive shaft A c M M s A τ = s A R Nte: τ = M/AcR here. Ski lift (pht curtesy P.M. Andersn) τ Chapter 7-4 ١

2 OTHER COMMON STRESS STATES (i) Simple cmpressin: OTHER COMMON STRESS STATES (ii) Bi-axial tensin: Hydrstatic cmpressin: A Canyn Bridge, Ls Alams, NM (pht curtesy P.M. Andersn) Balanced Rck, Arches Natinal Park (pht curtesy P.M. Andersn) = A Nte: cmpressive structure member ( < 0 here). Pressurized tank (pht curtesy P.M. Andersn) θ > 0 z > 0 ish under water < 0 h (pht curtesy P.M. Andersn) Chapter 7-5 Chapter 7-6 Tensile strain: = L Shear strain: θ x Engineering Strain L / w / L γ = x/y = tan θ Lateral strain: L = L w Typical tensile test machine extensmeter Stress-Strain Testing specimen Typical tensile specimen Adapted frm ig. 7., Callister & Rethwisch 3e. gauge length y 90º 90º - θ Adapted frm ig. 7. (a) and (c), Strain is always dimensinless. Chapter 7-7 Adapted frm ig. 7.3, (ig. 7.3 is taken frm H.W. Hayden, W.G. Mffatt, and J. Wulff, The Structure and Prperties f Materials, Vl. III, Mechanical Behavir, p., Jhn Wiley and Sns, New Yrk, 965.) Chapter 7-8 ٢

3 Elastic Defrmatin. Initial. Small lad 3. Unlad Elastic means reversible! bnds stretch return t initial Linearelastic Nn-Linearelastic Chapter 7-9 Plastic Defrmatin (Metals). Initial. Small lad 3. Unlad bnds stretch planes & planes still shear sheared Plastic means permanent! elastic + plastic linear elastic plastic plastic linear elastic Chapter 7-0 Linear Elastic Prperties Mdulus f Elasticity, E: (als knwn as Yung's mdulus) Hke's Law: = E E Mechanical Prperties Slpe f stress strain plt (which is prprtinal t the elastic mdulus) depends n bnd strength f metal Linearelastic simple tensin test Adapted frm ig. 7.7, Chapter 7 - Chapter 7-٣

4 E(GPa) 0 9 Pa Yung s Mduli: Cmparisn Metals Allys Tungsten Mlybdenum Steel, Ni Tantalum Platinum Cu allys Zinc, Ti Silver, Gld Aluminum Magnesium, Tin Graphite Ceramics Plymers Cmpsites /fibers Semicnd Diamnd Si carbide Al xide Si nitride <> Si crystal <00> Glass -sda Cncrete Graphite Plyester PET PS PC PP HDPE PTE Carbn fibers nly CRE( fibers)* Aramid fibers nly ARE( fibers)* Glass fibers nly GRE( fibers)* GRE* CRE* GRE( fibers)* CRE( fibers) * ARE( fibers) * Epxy nly Wd( grain) Based n data in Table B., Cmpsite data based n reinfrced epxy with 60 vl% f aligned carbn (CRE), aramid (ARE), r glass (GRE) fibers. Plastic (Permanent) Defrmatin (at lwer temperatures, i.e. T < Tmelt/3) Simple tensin test: engineering stress, Elastic initially p Elastic+Plastic at larger stress permanent (plastic) after lad is remved plastic strain engineering strain, Adapted frm ig. 7.0 (a), 0. LDPE Chapter 7-3 Chapter 7-4 Yield Strength, y Stress at which nticeable plastic defrmatin has ccurred. when p = 0.00 y tensile stress, p= 0.00 engineering strain, Adapted frm ig. 7.0 (a), y = yield strength Nte: fr inch sample = 0.00 = z/z z = in Chapter 7-5 Yield strength, y (MPa) Yield Strength : Cmparisn Metals/ Allys Steel (440) qt Ti (5Al-.5Sn) a W (pure) Cu (7500) M (pure) cw Steel (440) a Steel (00) cd Al (606) ag Steel (00) hr Ti (pure) Ta (pure) a Cu (7500) hr Al (606) a Tin (pure) Graphite/ Ceramics/ Semicnd Hard t measure, since in tensin, fracture usually ccurs befre yield. Plymers dry PC Nyln 6,6 PET humid PVC PP HDPE LDPE Cmpsites/ fibers Hard t measure, in ceramic matrix and epxy matrix cmpsites, since in tensin, fracture usually ccurs befre yield. Rm temperature values Based n data in Table B.4, a = annealed hr = ht rlled ag = aged cd = cld drawn cw = cld wrked qt = quenched & tempered Chapter 7-6

5 TS y engineering stress Tensile Strength, TS Maximum stress n engineering stress-strain curve. Typical respnse f a metal strain engineering strain Metals: ccurs when nticeable necking starts. Plymers: ccurs when plymer backbne chains are aligned and abut t break. Adapted frm ig. 7., = fracture r ultimate strength Neck acts as stress cncentratr Chapter 7-7 Tensile strength, TS (MPa) Tensile Strength: Cmparisn Metals/ Allys Steel (440) qt W (pure) Ti (5Al-.5Sn) Steel (440) a a Cu (7500) Cu (7500) hr cw Steel (00) Al (606) ag Ti (pure) a Ta (pure) Al (606) a Graphite/ Ceramics/ Semicnd Diamnd Si nitride Al xide Si crystal <00> Glass-sda Cncrete Graphite Plymers Nyln 6,6 PC PET PVC PP LDPE HDPE Cmpsites/ fibers C fibers Aramid fib E-glass fib ARE( fiber) GRE( fiber) CRE( fiber) wd( fiber) GRE( fiber) CRE( fiber) ARE( fiber) wd ( fiber) Rm temperature values Based n data in Table B4, a = annealed hr = ht rlled ag = aged cd = cld drawn cw = cld wrked qt = quenched & tempered ARE, GRE, & CRE = aramid, glass, & carbn fiber-reinfrced epxy cmpsites, with 60 vl% fibers. Chapter 7-8 Ductility Plastic tensile strain at failure: Engineering tensile stress, Adapted frm ig. 7.3, smaller %EL larger %EL Engineering tensile strain, L L %EL = x 00 L Anther ductility measure: A A %RA = f x 00 A - f A L A f Chapter 7-9 L f Tughness Energy t break a unit vlume f material Apprximate by the area under the stress-strain curve. Engineering tensile stress, Adapted frm ig. 7.3, small tughness (ceramics) Engineering tensile strain, Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy large tughness (metals) very small tughness (unreinfrced plymers) Chapter 7-0

6 Resilience, U r Ability f a material t stre energy Energy stred best in elastic regin yi Elastic Strain Recvery D Adapted frm ig. 7.5, y U r = d 0 If we assume a linear stress-strain curve this simplifies t U r y y Chapter 7 - y Stress Adapted frm ig. 7.7,. Lad Elastic strain recvery. Unlad 3. Reapply lad Strain Chapter 7 - True Stress & Strain Nte: S.A. changes when sample stretched True stress True strain T = A i T = lnl i ( l ) T T = = ln ( + ) ( + ) Hardening An increase in y due t plastic defrmatin. y y0 large hardening small hardening Adapted frm ig. 7.6, Chapter 7-3 Curve fit t the stress-strain respnse: T = K( T ) n hardening expnent: n = 0.5 (sme steels) t n = 0.5 (sme cppers) true stress (/A) true strain: ln(l/l ) Chapter 7-4

7 Elastic Shear mdulus, G: τ = G γ Elastic Bulk mdulus, K: P = -K V V Other Elastic Prperties τ G γ Special relatins fr istrpic materials: G = E ( + ν) P K E K = 3( ν) V P V M M P simple trsin test P pressure test: Init. vl =V. Vl chg. = V Chapter 7-5 Pissn's rati, ν: ν = L metals: ν ~ 0.33 ceramics: ν ~ 0.5 plymers: ν ~ 0.40 Units: E: [GPa] r [psi] ν: dimensinless Pissn's rati, ν L -ν ν > 0.50 density increases ν < 0.50 density decreases (vids frm) Chapter 7-6 Useful Linear Elastic Relatinships Simple tensin: = L = ν w L EA EA A w / L Simple trsin: α = ML π r 4 G M = mment α = angle f twist L Mechanical Prperties Ceramic materials are mre brittle than metals. Why is this s? Cnsider mechanism f defrmatin In crystalline, by dislcatin mtin In highly inic slids, dislcatin mtin is difficult few slip systems resistance t mtin f ins f like charge (e.g., anins) past ne anther r L / Material, gemetric, and lading parameters all cntribute t deflectin. Larger elastic mduli minimize elastic deflectin. Chapter 7-7 Chapter 7-8 ٧

8 lexural Tests Measurement f Elastic Mdulus Rm T behavir is usually elastic, with brittle failure. 3-Pint Bend Testing ften used. -- tensile tests are difficult fr brittle materials. crss sectin b rect. d R circ. L/ L/ Adapted frm ig. 7.8, = midpint deflectin Determine elastic mdulus accrding t: 3 L x E = (rect. crss sectin) 3 4bd slpe = 3 L E = (circ. crss sectin) 4 linear-elastic behavir πr Chapter 7-9 lexural Tests Measurement f lexural Strength 3-pint bend test t measure rm-t flexural strength. crss sectin b rect. d R circ. lexural strength: fs = 3 f L bd L f fs = 3 πr (rect. crss sectin) (circ. crss sectin) L/ L/ lcatin f max tensin Adapted frm ig. 7.8, = midpint deflectin Typical values: Material fs(mpa) E(GPa) Si nitride Si carbide Al xide glass (sda-lime) 69 Data frm Table 7., Chapter 7-30 Hardness Resistance t permanently indenting the surface. Large hardness means: -- resistance t plastic defrmatin r cracking in cmpressin. -- better wear prperties. e.g., 0 mm sphere mst plastics brasses Al allys D apply knwn frce d easy t machine steels file hard increasing hardness measure size f indent after remving lad cutting tls Smaller indents mean larger hardness. nitrided steels diamnd Chapter 7-3 Hardness: Measurement Rckwell N majr sample damage Each scale runs t 30 but nly useful in range Minr lad 0 kg Majr lad 60 (A), 00 (B) & 50 (C) kg A = diamnd, B = /6 in. ball, C = diamnd HB = Brinell Hardness TS (psia) = 500 x HB TS (MPa) = 3.45 x HB Chapter 7-3 ٨

9 Hardness: Measurement Variability in Material Prperties Table 7.5 Elastic mdulus is material prperty Critical prperties depend largely n sample flaws (defects, etc.). Large sample t sample variability. Statistics Mean n Σ x x = n n Standard Deviatin n Σ s = where n is the number f data pints ( x x ) i n Chapter 7-33 Chapter 7-34 Design r Safety actrs Design uncertainties mean we d nt push the limit. actr f safety, N Often N is y between wrking =. and 4 N Example: Calculate a diameter, d, t ensure that yield des nt ccur in the 045 carbn steel rd belw. Use a factr f safety f 5. d y wrking = 045 plain N carbn steel: y = 30 MPa L 0,000N 5 TS = 565 MPa π( d / 4) = 0,000N d = m = 6.7 cm Chapter 7-35 Summary Stress and strain: These are size-independent measures f lad and displacement, respectively. Elastic behavir: This reversible behavir ften shws a linear relatin between stress and strain. T minimize defrmatin, select a material with a large elastic mdulus (E r G). Plastic behavir: This permanent defrmatin behavir ccurs when the tensile (r cmpressive) uniaxial stress reaches y. Tughness: The energy needed t break a unit vlume f material. Ductility: The plastic strain at failure. Chapter 7-36 ٩